If the name change was mission oriented in nature, she would have reverted back later. The fact she didn't clearly infers that it was her preference to remain a Grey. The most compelling on panel evidence for why that might be is her reaction to Scott and Emma's ship as seem in X-Men Unlimited #11. She manifested the PF and trashed the restaurant she and Havok were in when discussing the whole thing. The motivation seems clear.
Years later she was fine with it yes, but you'll note that she retains the Grey name. There's a reason for that.